The time period of oscillation of a freely suspended bar magnet with usual notations is given by

1. $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{I}}{{\mathrm{MB}}_{\mathrm{H}}}}$

2.  $T=2\mathrm{\pi }\sqrt{\frac{M{B}_H}{I}}$

3. $T=2\sqrt{\frac{\mathrm{I}}{{\mathrm{MB}}_{\mathrm{H}}}}$

4. $T=2\mathrm{\pi }\sqrt{\frac{B_H}{MI}}$

Time period for a magnet is T. If it is divided in four equal parts along its axis and perpendicular to its axis as shown then time period for each part will be

1. 4T

2. T/4

3. T/2

4. T

The period of oscillation of a magnet in vibration magnetometer is 2 sec. The period of oscillation of a magnet whose magnetic moment is four times that of the first magnet is

(1) 1 sec                         

(2) 4 sec

(3) 8 sec                         

(4) 0.5 sec

If a magnetic needle is made to vibrate in uniform field \(H\), then its time period is \(T\). If it vibrates in the field of intensity \(4H\), its time period will be:

A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where dip angle is 30^o and 15 oscillations per minute at a place where dip angle is 60^o. The ratio of total earth's magnetic field at the two places is:

1. $3\sqrt{3}:8$
2. $16:9\sqrt{3}$
3. 4:9
4. $2\sqrt{3}:9$

A magnet of magnetic moment M oscillating freely in earth's horizontal magnetic field makes n oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled, the number of oscillations made per minute would be

1. $\frac{n}{2\sqrt{2}}$                         2. $\frac{n}{\sqrt{2}}$

3. $2\sqrt{2}n$                        4. $\sqrt{2}n$

Magnets \(A\) and \(B\) are geometrically similar but the magnetic moment of \(A\) is twice that of \(B\). If \(T_1\) and \(T_2\) be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then \(\frac{T_1}{T_2}\) will be:
1. \(\frac{1}{3}\)
2. \(\frac{1}{2}\)
3. \(\frac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)

A magnetic needle suspended by a silk thread is vibrating in the earth's magnetic field. If the temperature of the needle is increased by 500°C, then

(1) The time period decreases

(2) The time period remains unchanged

(3) The time period increases

(4) The needle stops vibrating

The time period of oscillation of a bar magnet suspended horizontally along the magnetic meridian is T₀. If this magnet is replaced by another magnet of the same size and pole strength but with double the mass, the new time period will be

(1) $\frac{T_0}{2}$                           

(2) $\frac{T_0}{\sqrt{2}}$

(3) $\sqrt{2}{T}_0$                        

(4) 2T₀

The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by 19%. By doing this the periodic time of the magnetometer will

1. Increase by 19%       2. Decrease by 19%

3. Increase by 11%       4. Decrease by 21%